An attempt to describe heart attacks via continuum damage mechanics (Archives of Mechanics - Test, 2000)
In an earlier paper the author expressed evolution equations of classical continuum damage mechanics in terms of unit dissipated power and proposed an extension to biological materials in vivo, adding a term describing recovery. In the present paper an analogy with evolution of coronary artery disease is established. If we denote by S (relative stenosis) one minus the ratio of current luminal area to the initial area, then the condition S = 1 at a certain point of the artery means complete blockage at this point resulting in a heart attack (myocardial infarction). This corresponds to the condition of critical state D = 1 in damage mechanics, where D denotes a scalar measure of damage. Making use of this analogy, an evolution equation for S is proposed with unit dissipated power replaced by unit power of flow in individual cross-sections of coronary arteries and, subsequently, by the heart power. Further, another evolution equation describes the required heart power in terms of external loadings acting on the organism as a whole. Numerical integration of the evolution equations proposed makes it possible to distinguish loadings leading to a myocardial infarction from those subject to recovery. Also, the description of stable and unstable angina pectoris is discussed and illustrated by numerical examples.